Model Surface

On the surface, a film is growing.

Gaseous atoms, ejected from a heated coil of platinum, fall like snowflakes, alight, cool to solidity, and stick. They gather in clusters.

As new atoms land and attach themselves, the clusters grow; soon they begin to coalesce. The gaps between them shrink and keep shrinking; finally—phip!—the gaps disappear, and a first layer is complete. A second begins to form across its top.

The process of a thin film's evolution, at this remove, seems remarkably straightforward: as ordered and inevitable as bricklaying. But look still closer—with the aid of a tremendously powerful microscope—and you begin to see something else: A world of variety, a complicated terrain where atoms skitter and dance, where the crystalline solidity of a metal is broken by pits and hummocks and irregularities, where physics and chemistry collide.

Scientists got their first glimpse of the world of the surface in 1968, when Erwin Mueller, a chemist working at Penn State, developed the field-ion microscope, an instrument which could resolve, even manipulate, individual atoms. Since Mueller's day, there has been a proliferation of similar scopes: tools that allow us to see and alter the structure of the surface.

There have been parallel developments in technologies for growing films. Today, sophisticated deposition techniques enable construction of crystalline solids a single layer at a time.

These combined advances have opened the door to a whole new class of microengineered materials: devices designed and built at atomic scale.

In order to realize such devices, however, materials scientists and engineers first need a better grasp of the dynamic surface of a growing film. How do atoms and molecules get around? What governs their movement and where they end up?

"The modern challenge in understanding films," says Kristen Fichthorn, Penn State assistant professor of chemical engineering, "is understanding kinetics."

# Thin films—from one molecule to several hundred molecules thick—can be made out of diverse materials: metals, ceramics, silicon, diamond. They are the stuff of many high-tech industries: Thin films are employed in computer chips, compact disks, tool coatings, optical lenses and video cassettes, among countless other applications.

engineering properties for which thin films are prized—electrical conductivity, chemical reactivity, hardness, transparency—depend on their surface structure. Indeed, their chief attribute—their thinness—means that surface is virtually all there is to thin films. In industrial terms, a smooth film—a regular, unflawed surface—is a useful film.

Structure, in turn, depends on the conditions under which a film is grown.

Atoms deposited on a surface are charged with thermal energy. Seeking the security of equilibrium, they diffuse: they hop along the surface, dissipating their excess heat until they find a good place to settle.

This wandering is known as the random walk. "There is an equal probability of the atom's going in any direction," Fichthorn explains. "It's like a drunk."

Diffusion is strongly influenced by surface temperature. At high enough temperatures (in the case of metals, around room temperature; for silicon, much higher), arriving atoms will tend to settle in rather orderly fashion, finding their way down to the lowest unfilled layer of an evolving film where they will join themselves to an existing cluster or island; the resulting growth will be regular and smooth. At lower temperatures, however, the atoms grow truculent; their mobility is less: Instead of joining an island's outward expansion a freshly landed atom may perch on top of the island—and another may perch on top of it. The result is clumping and unevenness.

Another critical factor is deposition rate: the number and frequency of incoming atoms hitting the beach. If too many atoms are landing too fast, they can be thrown off their normal behavior; they may not have time to settle in the way they would like. Bumping into each other before they cool, they'll stick to one another and form smaller islands instead of finding and joining larger ones. Again, the result can be a bumpy film.

Such, anyway, is the standard model. And since the late '60s, the field-ion microscope and its younger cousins—including, particularly, the scanning tunneling microscope—have been bringing back evidence to support this view: atoms hopping the surface within a given area, faster or slower depending on the temperature.

Increasingly, however, the super scopes have also been showing things that don't seem to fit. Things that suggest kinetic activity not explained by standard theory. "Surprises keep coming up," is the way Fichthorn puts it.

One such surprise occurred in 1991, when a team led by W. F. Egelhoff, a researcher at the National Institute of Standards, observed something that hadn't been seen before: smooth, layer-by-layer growth of a film of copper at exceedingly low temperatures—as low as 80 degrees Kelvin. (273 degrees K equals zero degrees Celsius; 0 degrees K is absolute zero.) Egelhoff went on to demonstrate similar growth in several other metal "systems."

Other researchers began making parallel observations. "What some of them actually saw," says Fichthorn, "was re-entrant growth—smooth at low temperatures, not smooth at room temperature, and smooth again at high temperatures."

Egelhoff's explanation for this "new" kind of growth was something called the transient mobility model. "What it says," Fichthorn explains, "is that an atom coming in at a high velocity and hitting a cold surface may not dissipate its energy very quickly—it may be able to hop across the surface more than we might expect, until its excess energy is gone." What transient mobility would mean for film growth, Fichthorn continues, is that an incoming atom would not be likely to get stuck on top of an existing island, for example. "It would have enough energy to diffuse off the edge of the island and get to a lower layer."

In 1992, Fichthorn and her students set about to test the idea of transient mobility.

# Fichthorn, a theorist, does not work with microscopes, atomic or any other variety. Her medium of exploration is the computer model. A mathematics whiz since high-school days, Fichthorn came to Penn State in 1990 from a postdoctoral appointment at the University of California at Santa Barbara, and was promptly named a Presidential Young Investigator by the National Science Foundation.

"What I do," she explains, "is called atomistic simulation."

By weaving an intricate web of calculations, Fichthorn can simulate growth on the surface, focusing on the behavior of a small sub-set of atoms; through the computer she can "see" directly events that microscopes can image only indirectly or with considerable difficulty.

"The experimental analogues to what I do are mega, mega expensive," Fichthorn says. "You have to keep a chamber at ultra-high vacuum. For your results to have value, you have to have the face of your crystal well-defined, no contaminants. You need very sophisticated equipment."

Fichthorn's surface, by contrast, shows up on her computer screen as a rectangular slab made up of a tight phalanx of bright yellow balls, 10 layers deep. Using a technique called molecular dynamics, Fichthorn simulates what happens when a gaseous atom—a blue ball—impinges on the slab. She works mostly with simulations of platinum and copper, systems simple enough that their surface events can be well-defined.

With this mathematical mock-up, Fichthorn runs "experiments." She can check out hypotheses. She can manipulate conditions, and see what effects such tweaking might have in reality. She can predict events: show the microscopists trends and phenomena to look out for. Her calculations make a smart complement to the painstaking observations recorded by the instruments in the lab.

"What she gets," says Paul Weiss, a Penn State chemist and experimentalist collaborator with Fichthorn, "is a better picture of the mechanics—of how things happen." Weiss, on the other hand, uses his scanning tunneling microscope to measure actual rates and distances of motion. "Then," he says, "we can compare results."

Fichthorn quickly determined that Egelhoff's transient mobility wasn't enough to explain the growth of smooth film at low temperatures. Her calculations show, she says, that transient mobility doesn't happen—or at least not to the extent that Egelhoff suggested it should. She has gone on to predict the existence of other kinds of surface events that might explain re- entrant growth. The first of these she calls "capture."

In her model, Fichthorn has shown that when an incoming atom lands within a certain critical distance of an existing cluster, or island, that atom is quickly gobbled up, drawn into the cluster. Its random walk is cut short. "This has definite ramifications for film morphology," she says. "Capture affects the size distribution of islands in the early stages of growth. This in turn affects multilayer growth."

Clued by Fichthorn's finding, Gert Ehrlich, a researcher at the University of Illinois, recently found a real-life example of capture, using a field-ion microscope. "They deposited atoms at different distances from the perimeter of a cluster, then observed their positions after a three-second interval. What they saw was that atoms deposited within the critical distance were sucked in."

Another surface phenomenon, "push-out," as Fichthorn explains, had been hypothesized by experimentalists for some time, but no one had been able to devise a way to observe it. "We used our simulation to see whether it could happen," she says. "Turns out it can."

Push-out occurs when an incoming atom, landing atop an existing cluster, actually dislodges an atom already in place, nosing it aside and assuming its position. Fichthorn's calculations showed, first, that push-out is a relatively gentle event, not the "knock-out" that some theorists had supposed. But "the most important thing we found," she says, was that an atom's ability to pull off this maneuver depends on the size and shape of the island it lands on.

"Push-out only happens near the edge of an island. On a small island, it is easy for an atom to dislodge the atoms underneath it. As the island gets bigger, it's harder for this to happen. An atom landing in the middle of an island has to make it to the edge, which takes time. When it finally gets there, it is harder for it to get over."

# Fichthorn's next goal is to develop a new model, one that is capable of stringing the newly discovered surface phenomena together, capturing the evolution of a film across real time. Because of its ultra-fine resolution, molecular dynamics cannot accomplish this feat.

"This is a highly detailed model," Fichthorn explains. "It solves Newton's equations of motion for each atom. The numerical method for something like this requires time steps in the range of femtoseconds." (A femtosecond is a million billionth of a second: 0.000000000000001 seconds.)

"That's the time-scale at which atomic motion is happening." At such detail, all a computer modeler can practically do is arrange the briefest of snapshots: Anything else would require too much computer time. "A microsecond would take months to simulate," Fichthorn says. "To simulate the growth of a film would take longer than my lifetime."

Ordinarily, the way modelers surmount this obstacle is by stepping backwards: after running molecular dynamics, they feed the essence of their close-up results into a more macroscopic model. To do this, they typically deploy a statistical method known as Monte Carlo.

A Monte Carlo model—the name refers to the gambling capital, in recognition of the method's central reliance on the concept of random chance—takes the rules derived by "lower-level" calculations like molecular dynamics, and sticks them into a broader framework, something called transition-state theory.

"You represent the surface as a checkerboard," Fichthorn explains, "and you look at individual squares. What is the atom at that site going to do? How is it going to move? There's randomness involved, but each move also depends on what is happening in the surrounding squares.

"If you accept the theory for doing these individual moves, you can derive the relationship between the time-scale of each micro-event and what we call clock time." Monte Carlo techniques, she concludes, can provide a "coarse-grain" simulation of a film's evolution.

However. "The problem with Monte Carlo is that sometimes it's hard to tell which events are essential to include. The assumptions you have to make may limit the accuracy of your results."

In order to create a more reliable picture of film growth, Fichthorn is working out a different approach. Instead of employing molecular dynamics and Monte Carlo one after the other, as most modelers do, she is trying to fuse them, bringing some of the accuracy of molecular dynamics and some of the speed of Monte Carlo to a single model. A middle way, she calls it. The approach is adapted from models used to look at thermodynamic properties of fluids.

"When you're growing a film," Fichthorn explains, "there are intervals where nothing important—nothing that's going to change the film's structure—is happening. Our method allows you to skip this non-productive time, and simulate only what is important for morphology. It finds the action." In essence, the new model follows the contours of molecular dynamics, solving Newton's equations and all. However, it can use much larger time steps. And unlike Monte Carlo, it does not require that all potential rate constants (the number can be in the tens of thousands) be calculated beforehand. Instead, Fichthorn says, "It finds the rate constant for each local environment as the calculation is running."

So far, she says, the new approach seems to work pretty well. "You lose some dynamical accuracy—we still have to find out just how much. But it appears to keep the important features."

# Fichthorn recently began to focus her models on another class of surface actors: not atoms, but molecules.

"People understand a good bit now about how atoms move," she explains. "Molecules are an open arena."

A glance at several complex bead-and-stick configurations sitting on her desk shows why. Here, the atoms are small plastic beads: Fichthorn holds up a yellow one between two fingers. To make molecules, the beads are linked together in chains of various lengths by thin stems representing chemical bonds.

"An atom," says Fichthorn, "has classically three ways to move." She picks up a bead, moves it along an imaginary plane: up, back, and diagonally.

"With a molecule, those same chemical bonds that make its properties interesting allow a much greater range of motion." Setting down the bead, she picks up a reticulated chain—a molecule—and push-pulls it this way and that. "They can rotate," she says, rolling the chain over. "They can do the wedding march." Here she steps the chain forward, one end, then the other. "They can do many things."

Pierre DeGennes, of the College de France in Paris, won the Nobel prize in 198X, in part for his introduction of a new model for the diffusion of polymers. In DeGennes' vision, these compound molecules wriggle across the surface segmentally, like snakes. Fittingly, he calls the motion "reptation."

More recently, Fichthorn says, there has been important work done at Stanford University on the movements of alkanes, basic organic molecules which are vitally important in petrochemicals.

"At Stanford, they measured diffusion as a function of how long the molecule was—the first study to try to link diffusion to structure. This raised some interesting questions."

Do alkanes diffuse rigidly, like logs? Do they bend in the middle? Do they tumble end over end, or roll? "It also raises questions about whether the tenets for diffusion of atoms hold true for something as complex as a molecule."

As it does for atoms, the standard theory for molecules says that when surface temperature is low, molecular diffusion remains local: A molecule will hop between neighboring binding sites, via the easiest energetic route.

"But this doesn't always happen. Sometimes molecules take long flights across the surface. This has been seen experimentally. So there's something wrong with the theory."

Fichthorn has simulated the movements of dimers, tiny, two- atom molecules. She has also looked at larger molecules, chains up to 20 carbons. "We're interested in seeing how the mechanism of diffusion changes as a function of chain length," Fichthorn says. "When does segmental motion start?"

Platinum growth on platinum, the film she most often simulates, is not a system whose solution will offer direct technological benefits. "Right now," she says, "the value is just the insight.

"But we're moving toward developing the ability to understand how morphology is related to processing conditions in real industrial applications."

Kristen A. Fichthorn, Ph.D., is assistant professor of chemical engineering and physics, 164 Fenske Laboratory, University Park, PA 16802; 814-863-4807. Fichthorn was named a Presidential Young Investigator by the National Science Foundation in 1990. Her research is funded by grants from the NSF and from the Petroleum Research Fund.

Last Updated September 01, 1995